In mathematics, a function is weakly harmonic in a domain if for all with compact support in and continuous second derivatives, where Δ is the Laplacian. This is the same notion as a weak derivative, however, a function can have a weak derivative and not be differentiable. In this case, we have the somewhat surprising result that a function is weakly harmonic if and only if it is harmonic. Thus weakly harmonic is actually equivalent to the seemingly stronger harmonic condition.
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| - Malforte harmonia funkcio (eo)
- Weakly harmonic function (en)
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| - Je analitiko, malforte harmonia funkcio estas malforta solvo de la Laplaca ekvacio. Tamen, la koncepto estas ekzakte ekvivalenta al tio de (ordinare) harmonia funkcio. (eo)
- In mathematics, a function is weakly harmonic in a domain if for all with compact support in and continuous second derivatives, where Δ is the Laplacian. This is the same notion as a weak derivative, however, a function can have a weak derivative and not be differentiable. In this case, we have the somewhat surprising result that a function is weakly harmonic if and only if it is harmonic. Thus weakly harmonic is actually equivalent to the seemingly stronger harmonic condition. (en)
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| - Je analitiko, malforte harmonia funkcio estas malforta solvo de la Laplaca ekvacio. Tamen, la koncepto estas ekzakte ekvivalenta al tio de (ordinare) harmonia funkcio. (eo)
- In mathematics, a function is weakly harmonic in a domain if for all with compact support in and continuous second derivatives, where Δ is the Laplacian. This is the same notion as a weak derivative, however, a function can have a weak derivative and not be differentiable. In this case, we have the somewhat surprising result that a function is weakly harmonic if and only if it is harmonic. Thus weakly harmonic is actually equivalent to the seemingly stronger harmonic condition. (en)
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